Two 112-L tanks are filled with gas at 330 K. One contains 5.00 mol of Kr, and the other contains 5.00 mol of O 2 . Considering the assumptions of kinetic–molecular theory, rank the gases from low to high for each of the following properties. (c) Average speed

Welcome back everyone. Two containers with a volume of 150 L are filled with a gas at 350. Kelvin, one container holds five moles of organ while another holds five moles of carbon monoxide based on kinetic molecular theory, which gas has a faster average speed. Let's recall that the average speed, the average can be calculated as square root of eight multiplied by the universal gas constant multiplied by the absolute temperature divided by pi multiplied by the molar mass. M. What we can see from here is that since we have the same temperature for each condition, the only variable that matters is the molar mass that the average speed is inversely proportional to the square root of the molar mass, meaning the lower the molar mass, the higher the average speed. So we essentially want to compare the molar mass of organ which is 39.95 to the molar mass of carbon monoxide. The molar mass of carbon monoxide would be 28.01. So which one is lower? Well, 28.01 is lower than 39.95. And based on the fact that the molecules of co are lighter than the molecules of Argan. This would produce a higher average speed at the same temperature. And therefore our answer is co or carbon monoxide, carbon monoxide would have a faster average speed than organ because it is lighter. Thank you for watching.

Ch.10 - Gases: Their Properties & Behavior

McMurry8th EditionChemistryISBN: 9781292336145Not the one you use?Change textbook

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McMurry 8th Edition

Ch.10 - Gases: Their Properties & Behavior

Problem 10.108c

Chapter 10, Problem 10.108c

Two 112-L tanks are filled with gas at 330 K. One contains 5.00 mol of Kr, and the other contains 5.00 mol of O₂. Considering the assumptions of kinetic–molecular theory, rank the gases from low to high for each of the following properties.
(c) Average speed

Verified step by step guidance

Step 1: The average speed of a gas molecule is given by the equation: \(v_{avg} = \sqrt{\frac{8kT}{\pi m}}\), where \(k\) is the Boltzmann constant, \(T\) is the temperature in Kelvin, and \(m\) is the molar mass of the gas.

Step 2: The molar mass of Kr is 83.798 g/mol and the molar mass of O₂ is 32.00 g/mol. Convert these values to kg/mol by dividing by 1000, as the molar mass in the equation should be in kg/mol.

Step 3: Substitute the values of \(k\), \(T\), and \(m\) into the equation for each gas. Note that the temperature and the Boltzmann constant are the same for both gases, so the average speed is inversely proportional to the square root of the molar mass.

Step 4: Since O₂ has a lower molar mass than Kr, it will have a higher average speed.

Step 5: Therefore, the gases ranked from low to high average speed are Kr and then O₂.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Kinetic Molecular Theory

Kinetic Molecular Theory explains the behavior of gases in terms of particles in constant motion. It posits that gas particles are far apart, move freely, and collide elastically. This theory helps in understanding how temperature and mass affect the speed of gas particles, which is crucial for comparing the average speeds of different gases.

Graham's Law of Effusion

Graham's Law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. This means lighter gases will effuse faster than heavier gases. This principle is essential for determining the average speed of gases, as it allows us to compare the speeds of Kr and O2 based on their molar masses.

Root Mean Square Speed

The root mean square speed (rms speed) of a gas is a measure of the average speed of gas particles and is calculated using the formula v_rms = sqrt(3RT/M), where R is the gas constant, T is the temperature in Kelvin, and M is the molar mass. This concept is vital for ranking the average speeds of different gases, as it directly relates to their temperature and molar mass.

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